## An EOQ model for items with finite rate of production and variable rate of deterioration.(English)Zbl 0622.90031

The differential equations describing the inventory process Q(t) in the interval [0,T] are given by d Q(t)/dt$$+atQ(t)=K-R$$ $$(0\leq t\leq t_ 1)$$; $$dQ(t)/dt+atQ(t)=-R$$ $$(t_ 1\leq t\leq t_ 1+t_ 2)$$; $$dQ(t)/dt=-R$$ $$(t_ 1+t_ 2\leq t\leq t_ 1+t_ 2+t_ 3)$$; $$dQ(t)/dt=K-R$$ $$(t_ 1+t_ 2+t_ 3\leq t\leq t_ 1+t_ 2+t_ 3+t_ 4=T)$$ with the conditions: $$Q(0)=0$$, $$Q(t_ 1)=S$$, $$Q(t_ 1+t_ 2)=0$$, $$Q(t_ 1+t_ 2+t_ 3)=-P$$ and $$Q(t_ 1+t_ 2+t_ 3+t_ 4)=0$$ where a, K, R are given constants $$(0<a<1$$, $$K>R$$. R denotes the demand rate and K the production rate).
The constants S and P and the time points $$t_ i$$, $$i=1,...,4$$ are treated as the decision variables.
The authors describe a method of minimizing the total average cost for a production cycle in a case when the unit carrying, shortage and production costs are expressed by some known constants.
Reviewer: R.Rempala

### MSC:

 90B05 Inventory, storage, reservoirs